Solution: Energy Dissipation

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For this problem, we use conservation of energy to equate the kinetic energy and the frictional dissipation to determine the displacement of the cue when it comes to rest.

E_i = E_f
(1/2)mv² = f_kDx
(1/2)v² = m_kgDx
(1/2)(10²) = 0.25gDx
Dx = 20
20m > 8m, hence yes, the cue will hit the rail.
*Notice that mass was canceled in the equation and thus it is an independent factor in this problem*

Answer: Yes